A Cross-Country Comparison of Labor

Market Frictions

Geert Ridder�

Gerard J. van den Bergy

May 1, 2000

Abstract

In this paper we de�ne and estimate measures of labor market imper-

fection in the context of an equilibrium search and matching framework.

The method uses readily available data on distributions of unemployment

and job durations and wages. We estimate an index of search frictions,

the magnitude of structural and frictional unemployment, and the aver-

age monopsony power of �rms, and we examine the e�ect of the minimum

wage, unemployment bene�ts and search frictions on monopsony power.

Estimation of some of the characteristics is invariant to the way in which

wage determination is modeled. We perform separate empirical analyses

for the USA, the UK, France, Germany and the Netherlands.

�The Johns Hopkins University, Baltimore, USA and Center, Tilburg, The Netherlands.

E-mail: gridder@jhu.edu. Address: Department of Economics, The Johns Hopkins University,

Baltimore, MD 21218, USAyFree University Amsterdam, Tinbergen Institute, CEPR and CREST. E-mail:

gberg@econ.vu.nl.

Keywords: wages, search frictions, cross-country comparisons, unemployment, monopsony

power, minimum wage.

Earlier versions of this paper had the title \Estimating Measures of Labor Market Imperfection

for Five OECD Countries, Using Aggregate Data in an Equilibrium Search Framework". We

thank Niels de Visser for his excellent research assistance. Useful comments were provided by

seminar participants at NYU, UPenn, Penn State, UCL, Johns Hopkins, Tilburg, Queen's, IZA-

Bonn, Uppsala, and Groningen, and by participants at the ESEM 1997, SOLE 1998, and CILN

1998 conferences, in particular by John Kennan. We thank INSEE-CREST for the permission

to use the Enquete Emploi data.

1 Introduction

Labor economists have accumulated evidence that is at odds with the view that

the labor market is a standard competitive market, where in equilibrium the

wage is equal to the value of the marginal product of the worker. This evidence

shows that wages are positively related to the number of employees of the �rm

or establishment, even if one controls for productivity-related characteristics of

the workers (Brown and Medo�, 1989), and that the wages in di�erent industries

di�er persistently (Krueger and Summers, 1988). These deviations from the

competitive equilibrium have been found for many countries. Evidence against

the simple competitive model in a frictionless world is also provided by the fact

that in many countries unemployment is persistent, and wage adjustments do not

restore the balance between labor demand and supply (see e.g. Layard, Nickell

and Jackman, 1991, for a survey).

Recently, a literature has emerged that stresses the importance of labor mar-

ket frictions and the resulting labor market ows, for understanding unemploy-

ment and wage determination (see Mortensen and Pissarides, 1999, for a survey).

The size of these ows is assumed to be a�ected by the behavior of employers

and employees, who make their decisions with incomplete information on the

opportunities in the market. The discovery of these opportunities is modelled

as the outcome of a random process, i.e. random from the point of view of the

individual employer or employee. The resulting delays are referred to as search

frictions or informational frictions. Such models are consistent with the observed

anomalies in wage determination, and also provide an explanation for persistent

unemployment.

It is well-known that the presence of search frictions gives employers a certain

amount of monopsony power. Basically, if �rms pay wages that are strictly

smaller than the value of the marginal product of the workers, then it is still

possible to maintain a positive workforce, because it takes time for the employees

to �nd a better paying job. The monopsony power depends on a number of

variables. First of all, if a mandatory minimum wage is imposed then in general

the amount of monopsony power decreases. As long as the minimum wage (or,

more generally, the institutional wage oor) does not exceed the value of the

match, it merely redistributes part of the rents of the match from the �rm to the

worker. Secondly, if the amount of search frictions decreases for employed job

seekers then this provides an incentive for a �rm to pay higher wages, because

otherwise the �rms paying a higher wage than this �rm would be able to increase

their workforce at the expense of this �rm. At the other extreme, if workers for

2

some reason cannot search on the job and if they have the same unemployment

income, then it is optimal for wage-setting �rms to o�er a wage equal to the

common reservation wage of the unemployed. O�ering a higher wage does not

increase their workforce, but it decreases their pro�ts. The resulting equilibrium

is then the same as in the model in which one �rm is a monopsonist in the labor

market: all �rms o�er a wage equal to the unemployment income (see Diamond,

1971).

The imposition of a minimum wage has the side-e�ect that it may induce

structural unemployment. In a segmented labor market consisting of segments

with di�erent productivity levels, the imposition of a minimum wage exceeding

the productivity level of a particular segment causes all �rms in that segment to

become unpro�table. All individuals associated with this segment then become

permanently (or structurally) unemployed. This side-e�ect of the minimum wage,

or wage oors in general, has widely been held responsible for at least part of the

European unemployment problem. Indeed, the di�erence between the European

and American labor markets is often phrased in terms of a choice between, on

the one hand, low wages and low unemployment, and, on the other, high wages

and high unemployment.

In this paper we examine the importance of labor market imperfections for

a number of countries. In particular, we estimate for each country (1) an index

of search frictions, (2) the amount of structural and frictional unemployment,

and (3) the average monopsony power of �rms. The index of search frictions is

de�ned as the mean number of job o�ers that a worker receives during a spell of

employment (that is, during a time period between two unemployment spells).

The larger this number, the less frictions there are for employed workers. This

number is of importance for wage determination: if it is large then it is relatively

easy for workers to leave a �rm for another �rm, so it re ects the bargaining

power of workers vis-�a-vis employers. The average monopsony power is de�ned

as the average fraction of the match value that is not paid to the worker. We use

data from �ve OECD countries: Germany, the Netherlands, France, the United

Kingdom and the USA.

The index of search frictions and the amount of frictional and structural un-

employment measure the distance from a competitive market without frictions.

For example, the amount of structural unemployment measures the quantity dis-

tortion induced by the wage oors in the economy. The monopsony power index

then measures the extent to which employers exploit frictions when they set their

wages, in the presence of a minimum wage. The actual value of this index can

be contrasted to the value if on-the-job search is impossible, or if a minimum

3

wage does not exist, or if frictions are absent (the competitive solution with zero

monopsony power). It should be noted that in a world in which �rms have to

pay search costs and job investment costs, the absence of frictions may actually

result in a less eÆcient equilibrium (see Caballero and Hammour, 1996).

Equilibrium search models provide a formal theoretical framework within

which the issues at hand can be analyzed. By now, there is a substantial litera-

ture in which these models are developed (MacMinn, 1980, Albrecht and Axell,

1984, Mortensen, 1990, Burdett and Mortensen, 1998), estimated (Eckstein and

Wolpin, 1990, Van den Berg and Ridder, 1998, Koning, Ridder and Van den

Berg, 1995, Bowlus, Kiefer and Neumann, 1995) or both (Bontemps, Robin and

Van den Berg, 2000). See Ridder and Van den Berg (1997) and Mortensen and

Pissarides (1999) for surveys. In this paper we rely on equilibrium search models

as an underlying theoretical framework. We will only be concerned with models

which allow for search on the job and are able to generate equilibrium wage dis-

persion. In e�ect, these will all be generalizations of the basic model developed

by Burdett and Mortensen (1998).

Estimation of equilibrium search models with longitudinal data is a non-trivial

task and requires data of high quality covering long time spans, as is obvious

from the empirical studies above. Such data are not readily available for every

country. In this paper we show that the measures of interest (which are related

to the fundamental parameters in equilibrium search models) can be estimated

from data collected in yearly cross-sectional surveys, such as the US Current

Population Survey (CPS) and the EC Labor Force Surveys (LFS). Most of the

information needed can be obtained from readily available OECD and EURO-

STAT publications that tabulate the marginal distributions of unemployment and

job durations and wages. It is surprising that the structural parameters of the

equilibrium search model can be estimated from marginal distributions, because

equilibrium search models simultaneously determine the unemployment and job

duration distribution and the distribution of wages. For example, the model stip-

ulates that the current wage and the wage o�er distribution a�ect the exit rate

out of a job, and that job o�er arrival rate in turn a�ects the shape of the wage

o�er distribution.

Thus, one of the contributions of this paper is the demonstration that the

measures of interest can be estimated from cross-section data. This is useful if

micro panel data are not available. Moreover, given the high requirements of the

quality of the longitudinal data and the relatively small number of observations

and high attrition rate in most longitudinal surveys, estimates derived from (re-

peated) cross-sections provide a useful comparison. Finally, and this is a subject

4

for further research, empirical research on models with an endogenous contact

rate requires a combination of time-series and cross-section information over a

period that exceeds the observation period of most panel studies.

Although we attempted to use only readily available data, we discovered that

the measure of search frictions is not estimable with suÆcient accuracy from the

marginal distribution of job durations. For that reason we explore whether the

observed joint distribution of job durations and earnings is more informative.

The relevant data are collected in the CPS in selected years and in some of the

European LFS.

Our estimation method is sequential and it closely follows the relation between

a certain measure and data on a particular variable. For example, we show that

data on marginal job durations (that is, job durations that are not conditioned

on the wage) allow us to estimate the index of search frictions, without the

need to estimate other parameters simultaneously. In some instances we use

all available degrees of freedom in the data, and it is perhaps more appropriate

to describe our inferences as calibration instead of estimation1. The relation

between a certain measure and data on a particular variable is often valid under

a wide range of models. This means that we do not have to con�ne ourselves to

one particular (equilibrium search) model. For example, estimation of the index

of search frictions from marginal job duration data only requires that employed

job seekers behave according to the partial on-the-job search model of repeated

search.

With additional assumptions, the estimates of the friction parameters are

used to compute factual and counterfactual measures of the degree of monopsony

power and to decompose wage variation into variation due to productivity dif-

ferences and variation due to search frictions. These additional assumptions are

on the nature of productivity variation, in particular whether these di�erences

are associated with workers or with �rms. To decide this issue we would need

micro panel data, and for that reason we consider the two extreme cases (all

productive di�erences are associated with workers and these workers operate on

distinct labor markets, and all productive di�erences are associated with �rms

and there are no separate markets) to bound our estimates.

In section 2 we introduce the equilibrium search framework. The estimation

procedure is described in sections 3-5. Section 6 discusses the data and the

estimation results. Section 7 contains the conclusions. In the Appendix we

1For that reason we do not report standard errors. In cases where there are fewer parameters

than observations, these standard errors depend on the details of the sample design of the CPS

and LFS, and these details are not available to us.

5

discuss our approach in the light of alternative assumptions.

2 The theoretical framework

2.1 The basic Burdett-Mortensen equilibrium search model

We use extensions of the homogeneous equilibrium search model of Burdett and

Mortensen (1998) and Mortensen (1990) to interpret the estimation results and

occasionally derive empirical equations. It is thus useful to review this basic

homogeneous model brie y. We do not claim that the basic model gives an

accurate description of the whole labor market. In subsection 2.2 we brie y

discuss extensions that are supposed to increase the degree of realism of the basic

model, notably by allowing for heterogeneity. Most of these extensions have been

developed in the recent literature (see references below).

The basic model considers a labor market consisting of a continuum of work-

ers and �rms. The measure of workers is denoted by m, and the measure of

unemployed workers by u. The measure of �rms is normalized to one.

The supply-side is equivalent to a standard partial job search model with

on-the-job search (see Mortensen, 1986). Workers obtain wage o�ers, which are

random drawings from the wage o�er distribution F (w), at an exogenous rate �0when unemployed and �1 when employed. Whenever an o�er arrives, the decision

has to be made whether to accept it or to reject it and search further for a better

o�er. Layo�s accrue at the constant exogenous rate Æ. The opportunity cost of

employment is denoted by b and is assumed to be constant across individuals and

to be inclusive of unemployment bene�ts. The optimal acceptance strategy for

the unemployed is characterized by a reservation wage � satisfying

� = b + (�0 � �1)Z1

�

1� F (w)

Æ + �1(1� F (w))dw (1)

Employed workers accept any wage o�er that exceeds their current wage. In

sum, workers climb a job ladder to obtain higher wages, but this e�ort may be

frustrated by a spell of (frictional) unemployment. Note that �1=Æ equals the

average number of job o�ers in a given spell of employment, since the average

duration of a spell of employment is 1=Æ, and job o�ers arrive according to a

Poisson process with parameter �1. This quantity is the index of search frictions

that is enters the distribution of wage o�ers. The optimal search strategies of

unemployed and employed workers together will be referred to as the repeated

search strategy.

6

Now consider the ows of workers that result if workers use repeated search.

First, note that �rms do not o�er a wage below �, so that all o�ers are acceptable

to the unemployed. Consequently, the ow from unemployment to employment

is �0u. The ow from employment to unemployment is Æ(m � u). In a steady

state these ows are equal and the resulting unemployment rate is

u

m=

Æ

Æ + �0(2)

Let the distribution of wages paid to a cross-section of employees have distri-

bution function G. These wages are on average higher than the wages o�ered,

because of the ow of employees to higher paying jobs. The stock of employees

with a wage less or equal to w has measure G(w)(m � u). In the steady state,

the ows into and out of this stock are equal, which implies that

G(w) =ÆF (w)

Æ + �1(1� F (w))(3)

Equations (1)-(3) and all equations that are derived from these relations only

depend on the repeated search strategy of the workers and the steady state equi-

librium condition. They are independent of the way that the model is closed by

wage setting by the employers. This fact is exploited in our empirical work.

Now consider optimal wage setting by the employer. We assume that the

marginal value product p does not depend on the number of employees, i.e.

we assume that the production function is linear in employment. Assume that

p > maxfb; wming, where wmin is the mandatory or legal minimum wage. The

�rm maximizes the steady-state pro�t ow, which is the pro�t per worker p� w

times the steady-state labor force of the �rm, which depends on F . Burdett and

Mortensen (1998) show that this game has a unique non-cooperative steady-state

equilibrium solution, with

F (w) =Æ + �1

�1

1�

sp� w

p� w

!

F has support (w;w), where w = maxf�; wming and w follows from F (w) = 1.

Furthermore,

G(w) =Æ

�1

sp� w

p� w� 1

!(4)

The equilibrium has some properties that are important for our purposes.

First of all, wages are dispersed, and all workers face a non-degenerate wage

o�er distribution. As a result, job-to-job transitions do occur. Secondly, �rms

7

always o�er wages that are smaller than their productivity level, so they do have

a certain monopsony power. Thirdly, the lowest wage in the market is either

the minimum wage or the reservation wage of the unemployed. The frictional

unemployment rate u=m does not have a \choice" component. Consequently, it

is fully determined by the magnitudes of the arrival rates �0 and Æ. Finally, note

that F and G only depend on �0; �1 and Æ by way of the ratios �0=Æ and �1=Æ,

which will be denoted by k0 and k1, respectively (�0 only a�ects wages by way

of �).

Because all workers and �rms are identical, the presence of wage dispersion

implies that the law of one price does not hold in equilibrium. However, we

obtain the competitive equilibrium, in which all wages are equal to p, and the

monopsonistic equilibrium, in which all wages are equal to maxfb; wming, as limits

of the equilibrium solution. If �0 approaches in�nity, i.e. if the unemployed �nd

jobs instantaneously, then they can a�ord to be extremely selective with respect to

wage o�ers. As a result, � approaches p, and the wage o�er and wage distributions

are degenerate in p. If �1 approaches in�nity, i.e. if the employed �nd jobs

instantaneously, then workers instantaneously move to the top of the wage ladder,

and the wage distribution G approaches the degenerate distribution at p. In this

case � does not approach p, and neither does F . However, this is irrelevant,

because an unemployed worker, upon leaving unemployment, immediately moves

to a wage p. As a result, �rm pro�ts are equal to zero (all this also holds if

k1 approaches in�nity). At the other extreme, if �1 (or k1) approaches zero,

i.e. if the employed do not receive alternative job o�ers, then the distributions

F and G are degenerate at maxfb; wming. In the (general) intermediate case,

the wage (o�er) distributions for larger k1 �rst-order stochastically dominate the

wage (o�er) distributions for smaller k1.2

In traditional monopsony models of the labor market, (p � w)=w is used as

a measure of the monopsony power of a �rm paying w. The value of (p� w)=w

can be shown to equal the relative increase in w needed for a 1% increase in the

workforce of the �rm. The latter is also true for the present model (Boal and

Ransom, 1997). In fact, we adopt (p � w)=p as our measure of the monopsony

power of a �rm paying w. This is of course a monotone transformation of (p �

w)=w. Note that in the present case wages are dispersed, so our measure of the

monopsony power in the labor market has to be based on an average value (see

section 5).

The basic equilibrium search model is a highly stylized model with strong im-

2This is true if � < wmin. If � > wmin and k1 is not very small then an increase in k1

decreases �, so until � decreases below wmin, the stochastic dominance is not of �rst order.

8

plications for the distribution of unemployment and job spells. Are these predic-

tions consistent with empirical evidence? Of course, not much should be expected

from a model that assumes that all workers and �rms are identical. In equilibrium,

all job o�ers are acceptable to the unemployed, and the re-employment hazard

is equal to the o�er arrival rate. This is consistent with the empirical evidence

in e.g. Devine and Kiefer (1991) and Van den Berg (1990). Although job search

models originally were introduced as a potential explanation for the existence of

unemployment, most empirical studies �nd that rejection of job o�ers is rare.

Note that the homogeneous model does not allow for structural unemployment.

The rate at which job spells end decreases with the wage. This is consistent with

empirical evidence (Lindeboom and Theeuwes, 1991). In equilibrium there is a

positive association between �rm size and wage. Hence, the model is consistent

with the employer size wage e�ect as well.3 However, the actual solutions for the

equilibrium wage (o�er) distribution have increasing densities. This implication

is at odds with the data. This means that the shapes of the empirical wage (o�er)

distributions are not explained by the model.

2.2 Extensions of the basic model

In this subsection we examine some extensions of the basic model. We focus

in particular on heterogeneity in the �rms' productivity levels p. As argued

in Ridder and Van den Berg (1997) and Bontemps, Robin and Van den Berg

(2000), heterogeneity in p is essential to obtain an acceptable �t to observed

wages. We restrict attention to issues that are of importance for our measures

of labor market imperfection. For sake of brevity we refer to the literature for

details on the derivation of the equilibria and other properties. The maintained

assumption is that all workers who are attached to a given labor market are

homogeneous in terms of their opportunity cost of employment.

Van den Berg and Ridder (1998) estimate versions of the Burdett and Mortensen

(1998) model in which the labor market is considered to consist of a large number

of segments. Each segment is a separate labor market of its own, and workers

and �rms in a particular segment are homogeneous. The segments are de�ned by

observed characteristics like occupation as well as by unobserved characteristics.

Each segment has its productivity level p, and in each market the equilibrium

is as in the basic model. Such between-market heterogeneity can be associated

with the worker or with the �rm. Here, we do not make a distinction between

these sources of heterogeneity, as our aggregate data do not allow us to do so.

3See also Kiefer and Neumann (1993) and Ridder and Van den Berg (1997).

9

We take the distribution function �(p) to describe how p is distributed across

the individuals in the population.

Allowing for between-market heterogeneity in p enriches the model by adding

the possibility of structural unemployment. In a given segment, as long as the

minimum wage is lower than p, the level of unemployment is independent of

the minimum wage. If wmin exceeds � then a further increase in the minimum

wage shifts the whole wage (o�er) distribution upwards. That is, it redistributes

the rents of the match by lowering the pro�ts of all employers and raising the

income of all workers. In e�ect, it decreases the monopsony power of �rms.

However, if the minimum wage exceeds the productivity p, then �rms will close,

and all workers become permanently (structurally) unemployed. (The same holds

if b > p, but this turns out to be empirically less relevant.)

The unemployment rate is equal to

u

m=

Æ

Æ + �0(1� �(wmin)) + �(wmin) (5)

The �rst term on the right-hand side of this equation re ects frictional unem-

ployment and the second-term structural unemployment.

Now consider within-market heterogeneity in p. Mortensen (1990) and Bon-

temps, Robin and Van den Berg (2000) examine models in which �rms that are

active in a given labor market have di�erent labor productivity levels p. As a

result, workers are more productive in one �rm than in another. This alters the

equilibrium solution. Mortensen (1990) assumes that the distribution of produc-

tivities is discrete, whereas Bontemps, Robin and Van den Berg (2000) assume

that this distribution is continuous. Without loss of generality we adopt the con-

tinuous case, because it provides more convenient expressions for the equilibrium

solution. The model by Mortensen (1990) has been estimated by Bowlus, Kiefer

and Neumann (1995). Bontemps, Robin and Van den Berg (2000) estimate their

continuous model and show that it is able to give a perfect �t to the cross-sectional

wage density for an appropriate choice of the productivity distribution.

The equilibrium is characterized as follows. As before, p is the marginal

revenue of employing a worker, and p does not depend on the number of workers

at the �rm. It is important to stress that the expressions for � and u=m and

for G(w) as a function of F (w) are exactly the same as in equations (1), (2)

and (3) above. This is because worker behavior conditional on F is the same

as in the basic model. We denote as p the lowest productivity of �rms which

make a non-negative pro�t and thus are active on the market, and as �(p) the

distribution of p among active �rms. Obviously, p � maxf�; wming (note that

the measure of active �rms is endogenous). Bontemps, Robin and Van den Berg

10

(2000) show that the non-cooperative steady-state equilibrium solution has the

following properties. First of all, as in the basic model, w = maxf�; wming.

Secondly, the wage o�er w � K(p) of a �rm with productivity p equals

K(p) = p�

264p�maxf�; wming

[1 + k1]2 +

Z p

p

dxh1 + k1�(x)

i2375 h1 + k1�(p)

i2(6)

Thus, more productive �rms o�er higher wages than less productive �rms. By

combining (6) with the reservation wage equation we obtain an expression for

w given p;�; b; �0 and �1. By invoking F (w) = �(K�1(w)), we also obtain the

expression for F (w). In general it is not possible to obtain closed-form expressions

for K(p); F (w) or G(w). As a special case, if �(p) is a uniform distribution

or an exponential distribution then a closed-form expression for K(p) can be

derived. However, in the last case there is no closed-form solution for K�1(w),

and therefore neither for F (w).

In equilibrium, wages are dispersed, and all workers face a non-degenerate

wage o�er distribution. As a result, job-to-job transitions do occur. It is clear

from equation (6) that the mapping K(p) from productivities to wage o�ers

depends on the amount of search frictions. In general, K(p) increases in k1. If

k1 = 0 then the distributions F and G are degenerate at maxfb; wming.

Firms always o�er wages that are smaller than their productivity level, so

they do have a certain monopsony power. Productivity dispersion a�ects the

distribution of this monopsony power across �rms. In particular, dispersion fa-

vors high-productivity �rms disproportionally relative to low-productivity �rms,

because any wage set by the latter necessarily lies in the narrow interval between

the minimum wage and the low productivity level itself. If the minimum wage

increases then unemployment is not a�ected in this model. Firms with a p below

the old and the new minimum wage close down, and workers move to �rms with

higher p. Hence, in a labor market with only within market heterogeneity there

is no structural unemployment.

It is straightforward to construct a model that allows for both within-market

and between-market heterogeneity in p. For example, consider a labor market

that consists of a number of segments, each of which has a within-market pro-

ductivity distribution with a bounded support, while the support itself varies

across segments. Then there is structural unemployment if the minimum wage

exceeds the upper bound of the support of the productivity distribution for some

segment. The distribution across segments of the upper bound of the support

11

determines the amount of structural unemployment.4

There are empirical facts that cannot be described by the equilibrium search

models considered here. In labor economics there has been a lively debate on the

positive relation between wages and labor market experience. The present model

only allows for wage growth due to transitions from lower to higher paying jobs.

Attempts have been made to construct an equilibrium search model in which �rms

o�er a wage-tenure pro�le, but thus far the resulting models have unappealing

empirical predictions (Burdett and Coles, 1993). It should be noted that Altonji

and Williams (1997), in the most recent contribution to the descriptive empirical

literature, convincingly argue that wage growth on the job is of a smaller order

of magnitude than was suggested in some of the earlier work.

A low value of Æ may be a result of stringent job protection laws, and thus

may re ect an important source of labor market frictions. For this reason, we do

not focus exclusively on �1=Æ as the index of search frictions, but we also examine

the value of �1. It should be noted that certain important features of the models

(notably the equilibrium wage distributions) are invariant to allowing Æ to be a

function of the current wage; see Ridder and Van den Berg (1997).

A convenient feature of the equilibrium search models reviewed so far is that

they can easily deal with taxation of wage income. Let w be the gross wage, i.e.

the wage paid by the employer, and let wN be the net after-tax wage received by

the worker. With proportional taxation at rate � and a �xed deductible d, we

have

wN = (1� �)w + �d

If the marginal tax rate is less than 1 then the net wage increases with the

gross wage. Employees base their acceptance decisions on net wages, and a

net wage o�er exceeds the current net wage if and only if the gross wage o�er

4In this paper we avoid the issue of eÆciency. Note that, in the equilibrium search model with

between-market heterogeneity, job-to-job mobility is a rent-seeking activity that has no e�ect

at all on eÆciency, whereas in the within-market heterogeneity model, job-to-job transitions

increase eÆciency because they allow workers to move to higher-productivity �rms. In reality,

an economy is a�ected by shocks, and high mobility also helps to absorb shocks that are

sector-speci�c and induce reallocation (Davis, Haltiwanger and Schuh, 1996). This suggests

that high values of �0; �1 and Æ are advantageous in case of shocks. On the other hand, the

theoretical literature on \job matching models" shows that it is possible to have an ineÆciently

high amount of mobility (see Pissarides, 1990, Caballero and Hammour, 1996, and Bertola and

Caballero, 1996). When a �rm creates a vacancy then it has to pay investment costs as well as

search costs, and as a result, worker and �rm behavior is not necessarily eÆcient. Note that

the models considered in these references do not allow for job-to-job transitions, but such an

extension would not invalidate this result.

12

exceeds the current gross wage. Hence, taxation has no e�ect on the wages

set by the employers, and all expressions mentioned so far apply. The only

di�erence concerns the reservation wage of the unemployed. If unemployment

income is not taxed, and b is net unemployment income, then (1) holds after

substitution of (b � �d)=(1� �) for b, with � the before tax reservation wage of

the unemployed.5 The before-tax reservation wage is the reservation wage that

is used in the determination of the lower bound of the wage o�er distribution.6

3 Inference on structural and frictional unem-

ployment

In sections 3{5 we discuss inference on the measures of labor market imperfection

using aggregate data. It is thus useful to start each section with a brief account

of the type of aggregate data that are typically available. Section 6 discusses the

data we actually use in more detail.

Inference on the index of search frictions and the average monopsony power

builds on inference on unemployment, so we start with the latter. Aggregate

unemployment data typically consist of (a) the unemployment rate, i.e. the size

of the stock of unemployed as a fraction of the labor force, and (b) the frequency

distribution of elapsed unemployment durations in the stock of unemployed. It is

clear that the unemployment rate does not allow us to identify both structural and

frictional unemployment. In the vein of subsection 2.2, the stock of unemployed

consists of two groups: the structurally unemployed with zero exit rate, and

the frictionally unemployed with exit rate �0. The latter group has a changing

composition, whereas the former does not.

Let the structural unemployment rate (as a fraction of the labor force) be

denoted by q. According to equation (5), q equals �(wmin). The amount of

structural unemployment as a fraction of total unemployment can then be ex-

pressed as q=(u=m), which will be denoted by �. (Consequently, the structural

5If unemployment income is taxed as wage income, the before-tax reservation wage is given

by (1).6Note that the deductible d lowers the before-tax reservation wage of the unemployed. In

our analysis we ignore variation in unemployment income b. Because on average b < wmin,

unemployment due to rejection of job o�ers is predicted to be absent. Micro-simulation models

suggest that there is variation in b (OECD, 1997), so that some unemployment may indeed be

caused by high reservation wages. If that is true, then a deductible that is conditional upon

employment, as the Earned Income Tax Credit in the US, may lower these high reservation

wages. We shall explore this issue in future work.

13

and frictional unemployment rates can be expressed as �u=m and (1 � �)u=m,

respectively.) Now consider a large sample from the stock of unemployed per-

sons. A fraction � has a zero exit rate and in�nite unemployment durations. A

fraction 1� � has an exit rate equal to �0. An in ow sample of these frictionally

unemployed has an unemployment duration distribution that is exponential with

parameter �0. It is well known that the corresponding distribution of elapsed du-

rations in the stock has the same distribution. We do not observe to what type

an unemployed individual belongs. Consequently, the observed distribution (t)

of elapsed durations t in the stock is a mixture of a degenerate distribution with

a single mass point at in�nity and an exponential distribution with parameter

�0. The survival function equals

(t) � 1�(t) = � + (1� �)e��0t

This is a discrete mixture of exponentials with two mass points, one of which is

�xed at zero. Aggregate data provide observations on the fraction of unemployed

in a �nite number of duration intervals [ti; ti+1). The corresponding probabilities

equal (ti+1) � (ti). Thus, the parameters �0 and � (and therefore q) can be

readily estimated.

Some comments are in order. First, in reality, no one has an in�nite elapsed

duration. The fraction � is estimated by comparing the fraction of unemployed

in the last (open) duration interval to the fraction predicted by an exponen-

tial distribution with parameter �0 �tted to the earlier duration intervals. For

most countries the open interval concerns durations that exceed two years, and it

seems reasonable to assume that a fraction of those unemployed are structurally

unemployed in the sense de�ned above. Secondly, it is clear that the model is

overidenti�ed, and speci�cation tests can be applied. In particular, we can �t

an unrestricted exponential mixture and compare its �t to the defective mixture

in the model with structural unemployment. Thirdly, structurally unemployed

individuals may be underrepresented in unemployment �gures. These individuals

will never �nd a job, so they may classify themselves as a nonparticipant when

being questioned on their labor market state. Some of them may also be counted

as disabled or retired (and as claiming disablement or retirement bene�ts), even

though they are still able and willing to work. Their underrepresentation may

have been less serious in the EC countries until 1992, because until that year

unemployed individuals who were willing and able to work, but who were not

looking for a job were counted as unemployed. Since 1992 these individuals are

considered to be nonparticipants, as they have always been in the US. This prob-

lem cannot be solved by adding all nonparticipants to the unemployed, because

14

the state of nonparticipation also includes individuals who are clearly not struc-

turally unemployed. For example, it includes all mothers who are at home full

time. The data do not enable a distinction between these di�erent groups of

nonparticipants. Therefore we cannot deal with this any further. In any case,

the structural unemployment rate may be underestimated because of this, and

the bias is likely to be larger in the US. Fourthly, the estimates of �0 and � will

in general show variation by year. In particular, they are expected to vary over

the business cycle. We investigate this by using data from several years.

Once �0 and � are estimated, it is trivial to obtain an estimate of Æ by em-

ploying equation (5), which can be rewritten as

u

m= �

u

m+ (1� �

u

m)

Æ

Æ + �0

Given data on the unemployment rate u=m, an estimate of Æ follows from this

equation.

4 Inference on the index of search frictions

We use k1, i.e. �1=Æ, as our index of search frictions. This index equals the

average number of job o�ers in a spell of employment. As shown above, it is

informative on the speed at which workers climb the job ladder, and thus on the

strength of the bargaining position of workers. Note that in all of the equilibrium

models considered, F (w) and G(w) depend on �1 only by way of k1. It is also

interesting to know the value of �1 itself, as it is a structural parameter (note

that the previous section provides an estimate of Æ).

According to equilibrium search models, k1 a�ects the wage (o�er) distribu-

tion. However, it is obvious that data on the wage distribution G alone do not

suÆce to identify k1, and Van den Berg and Ridder (1993) show that estimation

of k1 is problematic even if data on both G and F are available. We therefore

turn to data on job durations.

Published data contain information on a number of quantities that are related

to job durations and ows into and out of jobs. These quantities are unconditional

on the wage in the job. To derive their counterparts in the model we have to

integrate wages out of the job duration distribution. Besides inference based

on published data we consider inference based on the joint distribution of job

durations and wages.

We �rst consider unconditional (on wages) inference.

15

4.1 Unconditional inference

It is important to distinguish between three di�erent (unconditional) distributions

of job spells. They are de�ned for three di�erent populations. We distinguish

between (i) the population of workers who move from unemployment to employ-

ment at a given point in time, the E-in ow population, (ii) the population of

workers who start in a job at a given point in time, the J-in ow population, and

(iii) the population of workers who hold a job at a given point in time, the E-stock.

The J-in ow di�ers from the E-in ow, because the former contains workers who

make a direct job-to-job transition. For the in ow populations the conditional

distribution of job durations given the wage is

'(tujjw) = (Æ + �1F (w))e�(Æ+�1F (w))tuj (7)

The only di�erence is the distribution of w which is F (w) in the E-in ow, and

'(w) =k1

log(1 + k1)

f(w)

1 + k1F (w)(8)

in the J-in ow. The latter distribution holds if unemployed workers accept all

job o�ers and employed workers accept any job with a higher wage, and if worker

ows are in equilibrium (see the Appendix). If we integrate with respect to the

distribution of w we obtain

Proposition 1 (i) If unemployed workers accept all job o�ers and employed

workers accept any job with a wage higher than the current one, then the

density of the job duration tuj in the E-in ow is

'(tuj) =e�Ætuj

Æk1t2uj

h1 + Ætuj � (1 + Æ(1 + k1)tuj)e

�Æk1tuji=

1

�1

Z Æ+�1

Æze�ztujdz

(ii) If in addition worker ows are in equilibrium, then the density of job dura-

tions in the J-in ow, t�j, is

'(t�j) =1

log(1 + k1)

1

t�je�Æt�j

h1� e��1t�j

i=

1

log(1 + k1)

Z Æ+�1

Æ

1

z

hze�zt�j

idz

(iii) Under the same assumptions as in (ii) the density of job durations in the

E-stock, te, is

'(te) =Æ(1 + k1)

k1

Z Æ(1+k1)

Æ

1

ze�zte dz

16

The density in the E-stock is derived using the well-known relation between

stock and ow duration densities (see e.g. Ridder, 1984).7 The derivation of

the densities does not use the solution for the equilibrium wage o�er distribution

given in Section 2. Hence, the densities in the proposition remain valid if we

close the model in some other way. All densities can be expressed as a mixture

of exponential distributions with di�erent mixing distributions that in all cases

have a support [Æ; �1 + Æ].This implies that all unconditional duration densities

have a decreasing hazard rate. The support gives the limits of the conditional

hazard of the job duration given w (note that F (w) is between 0 and 1). For the

E-in ow the hazard decreases from Æ+ 12�1 to Æ, for the J-in ow it decreases from

�1= log(1 + k1) to Æ,and for the E-stock from Æ(1 + k1)(log(1 + k1))=k1 to Æ.

On average, job spells are much longer than unemployment spells. To obtain

a reasonable number of complete job spells, one must either rely on retrospective

information on elapsed job spells, or one must follow a cohort during a long

observation period. Retrospective information concerning a rather distant past

may be unreliable due to recall errors. We can avoid these biases by censoring

the job durations after a relatively short observation period. With censored data

inference is usually based on the hazard rate of the distribution. An alternative

method to obtain a direct estimate of this hazard rate is available in repeated

cross-section data. If the repeated cross-sections are conducted yearly we can

obtain a direct estimate of the hazard rate over some observation window by

computing the empirical hazard for this observation period.

In the sequel �(:) denotes a hazard. For all three job spell distributions the

hazard decreases to Æ for long job spells. If we censor the job spells after a

relatively short observation period we can not recover Æ from the hazard rate.

Hence we can only estimate �1 from the empirical job spell hazard.

If we take Æ as given (or determined as in Section 3), we can express the

observed job spell hazards in the three populations near 0 as

�uj � Æ =1

2Æk1 = g1(k1)

��j � Æ = Æk1

log(1 + k1)� Æ = g2(k1)

7In the E-stock, the wage is distributed according to G(w), which under the assumption of

equilibrium worker ows can be expressed in terms of F (see equation (3)). It is not diÆcult to

show that the distribution of te given the wage w on the job is then exponential and is identical

to the distribution of tuj given w in the E-in ow. This justi�es the practice in the descriptive

empirical literature on job durations to assume exponentiality of the conditional distribution

of elapsed job durations given the wage. To our knowledge our result has never been derived

in the literature.

17

�ej � Æ = Æ(1 + k1) log(1 + k1)

k1� Æ = g3(k1)

The left hand side of these equations can be estimated by the empirical hazard

rate for short job spells. By the delta method the accuracy (asymptotic variance)

of the resulting estimate of k1 is determined by the inverse of the derivatives of

g1; g2; g3. The derivatives satisfy g01 > g02 > g03, and hence data from the E-

in ow are more informative than data from the J-in ow which in turn are more

informative than data from the E-stock. To give an example: If the observed

�e(0)=Æ equals 2.2 then the implied k1 equals 5.5. But if the observed �e(0)=Æ

equals 2.4 then k1 equals 7.4. Thus, a 9% increase in the observed variable leads

to a 35% increase in the value of k1. Given the fact that published aggregate

data are rounded and also contain other measurement errors, a 9% error in the

value of an observable should not be considered as uncommon.

In the literature on job and worker ows, the \total worker reallocation rate"

is de�ned as �e(0) + Æ (see Davis, Haltiwanger and Schuh, 1996). Basically, this

measures the sum of the number of individuals who have just starting to work in

a new job and the number of individuals who have just entered unemployment.

Once k1 and Æ are estimated, it is straightforward to estimate this measure as well

(it equals Æ+ Æ(1+k1) log(1+k1)=k1). It can subsequently be decomposed into a

component due to transitions into and out of employment and a component due

to job-to-job transitions.

4.2 Conditional inference

If we observe the joint distribution of job spells and wages, how can we use these

data to make inferences on the index of search frictions? First, it should be

noted that this joint distribution can be obtained from cross-sectional data if we

are prepared to use retrospective information. The joint distribution is available

for (a subsample of the CPS) in selected years. It is also available for the EU

countries that have an LFS that collects information on wages. Although this

joint distribution (or the conditional distribution of job spells given wages) can

not be found in the published summaries of the CPS or LFS , we use it for

estimation of the index of search frictions, because the estimates based on the

marginal job duration distribution are sensitive to changes in the data used. In

particular, the estimates derived from the empirical hazard at short durations

may be biased, because the occurrence of relatively many short job spells cannot

be explained by our model, at least not without modi�cation.

18

From the transition rate of a worker who currently earns w, �1(1�F (w))+ Æ,

it is clear that the conditional distribution of job spells given w yields a direct

estimate of �1 as the coeÆcient of 1�F (w). To obtain the marginal job spell dis-

tribution we integrate with respect to the distribution of wages. We can compare

this to the estimation of the slope coeÆcient in the regression model y = �x+ "

from the marginal distribution of y if the marginal distribution of x is known.

The estimator of �, the ratio of the sample means of y and x, has (normalized)

variance �2

x2, compared to �2

x2for the OLS estimator that applies if x and y are

observed jointly. The �rst estimator can be very inaccurate if the sample mean

of x is small. In general, the gain in accuracy if the estimate is obtained from

the joint distribution can be large.

By the steady state condition for worker ows, we �nd

1

Æ + �1(1� F (w))=

1

Æ(1 + k1)+

k1

Æ(1 + k1)G(w)

Hence, the model of repeated search (and the steady state conditions) imply that

there is a linear relation between the average length of a job spell and the cdf

of earnings. Moreover, the ratio of the slope coeÆcient and the intercept is an

estimator of k1. This provides a direct test of the repeated search model as a

description of worker behavior.

The right-hand side of the inverse of this equation expresses the hazard rate

of a job spell given w as a function of the observable G, the distribution of wages

among employed workers. This cdf is directly estimable, either by the empirical

cdf of wages or by a parametric cdf. We use this hazard rate to estimate k1.

Note that assumptions on the wage distribution are not required. The esti-

mates are valid irrespective of the assumptions on wage determination and the

nature of heterogeneity that a�ects the dispersion of the wage distribution.

5 Inference on wages: average monopsony power

and variance decomposition

We de�ne the average monopsony power � as follows,

� =E(p� w)

E(p)(9)

in which we take expectations over individuals (instead of �rms), so we examine

monopsony power from the perspective of the worker. To quantify this measure,

19

it does matter which model of wage determination is adopted. Consider the equi-

librium search model with between-market heterogeneity in �rms' productivities.

In a homogeneous segment, in a cross-section of employed workers, wages are dis-

tributed according to G(w j p) as speci�ed in equation (4). As shown in e.g. Van

den Berg and Ridder (1998), the cross-section distribution of wages in a segment

with productivity p can be represented as

w = w(p) + (1� y)(p� w(p)) (10)

where y is a random variable with

E(y) =1

1 + k1;Var(y) =

k213(1 + k1)3

(11)

The notation w(p) for the lowest wage highlights that it may be a function of

productivity p (by way of the reservation wage �). Substitution of (10) and (11)

in (9) gives

� =1

1 + k1

E(p)� E(w(p))

E(p)

Hence, the only feature of the wage distribution that a�ects the degree of monop-

sony is the average of the lowest wage over all workers. Recall that in each segment

p > w(p). In the limiting case where wmin equals p for each segment, the value

of � attains its minimum value 0. Similarly, if k1 is in�nite then E(w) = E(p)

and again � = 0. If, on the other hand, k1 = 0 and w = 0 then � attains its

maximum value (which is 1), as a sensible measure of monopsony power should.

Let us examine w(p). We distinguish between two cases: (i) �0 > �1 , and

(ii) �0 � �1. Note that � <> b i� �0 <> �1. In all �ve countries the (average)

unemployment bene�ts b are lower than the minimum wage, although the di�er-

ence is small in e.g. Germany. In case (i), w(p) for the high productivity workers

is equal to their reservation wage that is larger than the minimum wage. The

lowest wage for the low productivity workers is the minimum wage,

w(p) = wmin if wmin � p � p0

= b+ (1� )p if p > p0

with

p0 =wmin � b

1� and

=(1 + k1)

2

(1 + k1)2 + (k0 � k1)k1(12)

20

In case (ii), the reservation wage of the unemployed is always smaller than the

minimum wage, so for all p

w(p) = wmin

As a result, in case (i) the wage oor is the minimum wage (low productivity

workers) or depends on unemployment bene�ts (high productivity workers). In

case (ii) the wage oor is independent of unemployment bene�ts (as long as they

do not exceed the minimum wage).

From equations (10) and (11)

E(wjp) =k1

1 + k1p+

1

1 + k1w(p)

Var(wjp) = (p� w(p))2k21

3(1 + k1)3

Taking the expectation with respect to p, we have

E(w) =k1

1 + k1E(p) +

1

1 + k1E(w(p)) (13)

Var(w) = E(Var(wjp)) + Var(E(wjp)) (14)

In section 6, we �t a (lognormal) distribution to the grouped wage distribution.

Next, we compute the mean and variance of the wage distribution. Finally, we

determine the mean and variance of the productivity distribution by equating

the estimated mean and variance to the expressions (13) and (14). In case (ii)

we obtain closed form expressions

E(p) =(1 + k1)E(w)� wmin

k1

Var(p) =3(1 + k1)

3Var(w)� k21(E(p)� wmin)2

k21(3k1 + 4)

In case (i), the result is a nonlinear system that involves the truncated moments

E(pkjp � p0), k = 1; 2. If we choose a lognormal distribution for p, we obtain a

nonlinear system in the parameters of this distribution, and this system can be

solved numerically. It is important to stress that in either case we consider the

distribution of p among workers instead of �rms: segments with many workers

have a large weight in the over-all wage distribution.

21

Equation (14) is the basis for a decomposition of wage variation. The �rst

term on the right-hand side is associated with \pure wage variation" (failure

of the law of one price due to positive and �nite search frictions). The second

term is associated with productivity dispersion. We shall compute the fraction

of total wage dispersion due to the �rst term.8 This is another measure for the

distance to a competitive equilibrium. If search frictions in employment vanish

(�1 !1), then wages approach productivity levels, the labor market equilibrium

approaches a competitive equilibrium, and the fraction of wage dispersion due to

search frictions vanishes.

The estimated parameters of the productivity distribution can be used to

compute a number of counterfactual monopsony indices. In particular, we con-

sider (i) the e�ect of reducing unemployment bene�ts, while leaving the minimum

wage una�ected, (ii) the e�ect of reducing the minimum wage, while leaving the

unemployment bene�ts una�ected, (iii) the e�ect of eliminating both the mini-

mum wage and unemployment bene�ts, and (iv) the e�ect of making search on

the job impossible. Note that the estimated productivity distribution is trun-

cated at the minimum wage. All counterfactuals that involve a reduction of the

minimum wage below its current level must be interpreted with care. Although

the structural unemployment rate is an estimate of the probability mass of the

productivity distribution below the minimum wage, the reduction of the mini-

mum wage lowers the truncation point of the productivity distribution, and the

e�ect of this extension on the monopsony index depends on untruncated density

at the new minimum wage. In general, the average productivity will decrease

with a decrease in the minimum wage. Because we do not want to rely on the

estimated productivity density below the truncation point, the counterfactuals

assume that the average productivity does not change with the minimum wage.

6 Data and results

The data on labor market ows are from OECD, EUROSTAT and US Depart-

ment of Labor publications (see e.g. OECD, 1993, 1997). Most of the data for the

EC countries are obtained from the yearly Labor Force Surveys (LFS), a stan-

8In case (ii) this equalsE(p� wmin)

2

E(p� wmin)2 + 3(1 + k1)Var(p)

where expectations are taken with respect to the distribution of p across individuals. Note that

if �1 !1 then this converges to zero, whereas for �nite nonnegative values of �1 this is strictly

positive.

22

dardized survey that is conducted in all EC countries. The LFS is comparable to

the Current Population Survey (CPS) from which the US data on labor market

ows and wages are obtained. Unfortunately, the LFS does not collect data on

wages for all countries. For the EC countries the frequency distribution of wages

was obtained from other surveys. This makes these data less comparable across

countries than the data on labor market ows. In particular, we must deal with

both before- and after-tax wage rates.

For the conditional (on wages) estimation of the o�er arrival rate when em-

ployed, we used data from the January 1991 supplement of the CPS and from

the 1991 French LFS (the Enquete Emploi). These data are not published and

were obtained from the micro data �les.

We examine �ve OECD countries: the Netherlands (NL), Germany (D),

France (F), United Kingdom (UK) and the USA. Some summary statistics that

characterize the labor markets in these �ve economies are reported in Table 1.

We perform separate empirical analyses with data from di�erent years, but the

benchmark results are with data from 1990 or 1991. The aggregate data are not

available in a uniform format, but fortunately our estimation procedure is exi-

ble in that respect. We start with the inference on �0, structural unemployment,

and Æ. Next, we consider estimation of �1 from job duration data, and �nally,

inference on the wage distribution.

6.1 Estimation of unemployment parameters

We use the following data:

Unemployment spells. The distributions of (elapsed) unemployment spells cat-

egorized in 6 intervals were obtained from the Labor Force Survey (NL, D, F,

UK).9;10 The data are for the years 1983{94.11 For the US the frequency distribu-

tion of (elapsed) unemployment spells was obtained from the Current Population

Survey. The spells are grouped in 4 intervals.12

Unemployment rate. We use the unemployment rate as reported in LFS (NL, D,

F, UK) and standardized unemployment rate as reported by the US Department

9The intervals are 0{3, 3{6, 6{12, 12{18, 18{24, and 24{ months.10From 1991 on the data are for East- and West-Germany, before that year only for West-

Germany.11For the Netherlands, the LFS did not record unemployment durations in 1984 and 1986.12In the US Department of Labor publications in 1995, the intervals are: less than 5 weeks

(1.15 months), 5{14 weeks (1.15{3.44 months), 15{29 weeks (3.44{6.20 months), and 29{ weeks

(6.20{ months).

23

of Labor in 1995. Comparison with the standardized unemployment rates re-

ported in the OECD Quarterly Labor Force Statistics (1997) shows that the LFS

rates are almost equal to the OECD rates,13 except for the Netherlands where

this only is true after 1991. Until that year the LFS rate is about 1.5% higher in

that country (we return to this below).

The parameters �0 and � are estimated by quasi ML. The estimates obtained

by maximizing the grouped duration likelihood are quasi MLE because neither

the LFS, nor the CPS is a simple random sample. Although the estimators are

consistent for a strati�ed sample, provided that the strati�cation variables are

exogenous, the standard errors depend on the details of the sample design. Note

that the grouped MLE is less sensitive to rounding errors in the unemployment

durations. The estimate of Æ is computed from the unemployment rate and the

estimates of �0 and � (see section 3).

The estimation results are given in Tables 2, 3 and 4. We use data from the

years 1990 and 1991 to estimate the friction parameters on the job, the monopsony

index, and to decompose the wage variation. These years may be unrepresen-

tative, and a comparison of the estimates of the unemployment parameters over

a longer tine period is informative. The design of the CPS in the US has not

changed much during the years 1983{94.14 The time series of the parameters of

the unemployment duration distribution, the structural unemployment rate, and

the job destruction rate show gradual changes during 1983{94. During 1983{89

the unemployment rate in the US fell by 45%, and unemployment increased and

decreased again during 1990{1994. The parameters of the unemployment dura-

tion distribution (�0 and �) and the structural unemployment rate are clearly

negatively (�0 ) and positively (� and structural unemployment rate) correlated

with unemployment. The job destruction rate has a small downward trend during

the observation period. The changes over time in the estimates are small.

The LFS, the EC counterpart of the CPS, started in 1983.15 In 1992 there

was a major overhaul that a�ected the unemployment data. In an attempt to

conform to the International Labor Organization (ILO) guidelines, all persons

who reported to be unemployed, but did not search actively for a job in a refer-

ence period, were no longer considered to be unemployed. The estimates of �013The OECD rates are yearly averages and the LFS rates measure unemployment in a refer-

ence week, which is a normal (no bank holidays) week in Spring.14There has been a major overhaul in 1995. Data from 1995 and later are not comparable to

data from earlier years.15There was an LFS before 1983, but the results are not comparable between countries and

years.

24

and � change dramatically during the �rst four years of the LFS. The unemploy-

ment rate in the EC countries was essentially constant in those years. The job

destruction rate is almost constant, as one would expect. After that initial period

the estimates change more gradually until 1992. It is likely that the dramatic

changes during the �rst four year are spurious. This suspicion is reinforced by

the dramatic changes in the estimates for 1992. The change in the de�nition of

unemployment eliminated a large fraction of the long-term unemployed. This is

re ected by lower estimates of �. Except for the Netherlands, the change in de�-

nition did not lower the unemployment rate. It is remarkable, that just as during

the start of the LFS, there is a convergence to the pre{1992 parameter values. In

1996 the estimates for �0 are .0582 (NL), .0838 (D), .109 (F), and .123 (UK), and

for � .12 (NL), .18 (D), .15 (F), and .21 (UK). It seems that the changes in the

estimates during 1983{87 and 1992{94 are survey design e�ects. Note that the

reuni�cation of Germany did not a�ect the estimates for 1991 nearly as much.

If we concentrate on the period 1988{1991, a period of decreasing unemploy-

ment, we notice a number of di�erences between the �ve economies. The US has

by far the most \dynamic" labor market. The o�er arrival rate is 5.5 times that

in the UK that has the most dynamic labor market among the EC countries.

The job destruction rate in the US is three times as large as that in the UK.

The structural unemployment rate in the US is about a third of that in (West-

)Germany that has the lowest rate in the EC. The total unemployment rates

in (West-)Germany and the US were about the same during those years. The

Netherlands has the highest level of structural unemployment, both as a fraction

of total unemployment and as a fraction of the labor force. The job o�er arrival

rate in that country is close to that in the UK. The Netherlands also has by far

the highest minimum wage (see Table 1). Except for the UK, there is a clear

relation between the level of structural unemployment and the minimum wage,

which is in line with the wage oor explanation of structural unemployment dis-

cussed in section 2. The relation between the estimates of the job destruction

rate Æ and the employment protection ranking of the OECD that re ects legal

restrictions on lay-o�s is even stronger. Less protection is associated with a larger

job destruction rate.

6.2 Estimation of the index of search frictions

First, we discuss the available data:

Job spells. Job duration data are scarcer than data on unemployment durations.

The LFS collects data on elapsed job durations, but these data are not published.

25

OECD (1993) contains the frequency distribution of elapsed job durations, cate-

gorized in 6 intervals, for all �ve countries. These distributions are not directly

comparable, because some have been obtained from special panel surveys (NL,

D) and the other from the LFS (F, UK) or CPS (US).16 Table 5.5 in OECD

(1997) contains more comparable data for all �ve economies. The distributions

of elapsed job spells are obtained from the 1995 LFS (NL, D, F, UK) and the

1996 CPS (US).17 For the Netherlands and Germany, the fraction of jobs with

an elapsed duration of less than 1 year is much smaller than in the distribution

derived from the micro panel data in OECD (1993). In the sequel we use the

1995/1996 data for the analysis with elapsed job durations.

Separation rates. In subsection 4.4, we argued that elapsed job duration data

may not very informative on k1.18 For that reason we also use separation rates

of newly created jobs to estimate this index. The data on these separation rates

are from OECD (1997). We mostly use the fraction of jobs with a duration less

than a year that are dissolved within a year. In particular, Table 5.10 in OECD

(1997) provides the separation rate from 1 year to 2 years, which is calculated

as the di�erence between the number employed with tenure less than 1 year in

1994 and the number employed with tenure between 1 and 2 years in 1995, as

a fraction of the former. In the estimates for the US, both numbers are from

1995.19 We denote the reported separation rate by s1 (for ease of exposition, we

use a year as the time unit in this exposition on the job spells).

Job spells by wage. In the January/February supplements of the CPS data on

job spells are collected. Unfortunately, the questions that refer to job spells, vary

over the years. In some years, e.g. 1992, the questions are even dropped from

the questionnaire. We use the answer to the question how long the employee has

been with his/her current employer. This was asked in January 1991 and 1996.

The duration is recorded in months if less than 1 year and in years if longer.

The CPS is a rotating panel with 4 months of participation, 8 months of no

interviews, and 4 more months of participation after which the household leaves

the panel. Wages are only recorded for the outgoing rotation groups in January,

16The data for NL and D are for 1990 and those for F, UK, and US for 1991.17Farber (1998) shows that the marginal distribution of elapsed job durations in the US has

remained fairly stable over time.18OECD (1997) reports data corresponding to E(te), and these obviously su�er from the same

problem as the grouped data on elapsed job durations. An additional complication with the

former data is that they are calculated by counterfactually assuming that all elapsed durations

in the duration class \larger than 20 years" have a true elapsed duration of 27.5 years.19Diebold, Neumark and Polsky (1997) show that the US separation rates for jobs with a

given tenure have remained very stable over time during the past decades.

26

i.e. the households that entered the panel in October 1990 and 1989. We make

no e�ort match the job spells for the other households to the wages that were

collected in other waves of participation. As a consequence, we have data on job

spells and wages for a supposedly random sample of one fourth from the January

1991 CPS. We retain employees who report a wage (the usual gross earnings on

the job including overtime) and work 35 hours or more per week. Of the 68131

persons who were employed in January 1991, 15096 reported a wage. Of these

13431 reported a job spell and 10909 had a workweek of 35 hours or more. These

observations are used in the sequel.

The Enquete Emploi, the French LFS, is also a rotating panel, but the house-

holds participate for three consecutive years. They are interviewed once per year.

In the �rst year data are collected on the spell with the current employer. The

duration is in months if shorter than 2 years and in years if longer. In 1991 27962

individuals were interviewed, and of these 14131 were employed; 10432 worked 35

hours or more per week; 10210 reported a monthly gross wage.20 We eliminated

some observations with very small and large wages (below 3000 and above 30000

French Francs) and for the remaining 9963 individuals, 9854 reported a job spell.

The estimates are based on this sample.

First, we consider the information in the separation rates. As argued in

subsection 4.4, these rates may give more accurate estimates than the incomplete

job spells. Extraction of an estimate of k1 from data on s1 is non-trivial. First

of all, the jobs sample is not a genuine J-in ow sample but rather a sample from

the stock of jobs with a duration less than one year. Secondly, the exit rate out

of jobs decreases within the interval considered. For these reasons, it is invalid

to estimate ��j(0) from the equality s1 = 1� exp(���j(0)). To proceed, we have

to derive the joint density in the E-stock of the elapsed job duration te and the

residual (or remaining) job duration tr. Note that te + tr equals the total job

duration of a spell in the E-stock. The observation s1 then equals

s1 = Pr(0 < tr < 1j0 < te < 1)

By analogy to the derivations in Section 4 it is easy to show that the joint density

of te; tr is proportional toZ w

w

k1

log(1 + k1)

f(w)

1 + k1F (w)e�(Æ+�1F (w))te (Æ + �1F (w)) e

�(Æ+�1F (w))tr dw

After some elaboration we obtain

20Net of employer contributions to bene�ts

27

s1 = Pr(0 < tr < 1j0 < te < 1) = 1�

R Æ+�1Æ

1z2e�z(1� e�z)dzR Æ+�1

Æ1z2(1� e�z)dz

Some comments are in order. First, note that if �1 # 0 then s1 = 1� exp(�Æ), as

is to be expected. This suggests that, to compare the information in s1 to that

in the normalized characteristics in subsection 4.4, one should examine (s1 �

(1� exp(�Æ))=(1� exp(�Æ)). A problem here is that this normalized version of

s1 still depends on Æ. For most plausible values of Æ, however, s1 will give less

accurate estimates than ��j(0) but more accurate estimates than �e(0). In fact,

the information in the separation rate sT � Pr(0 < tr < T j0 < te < T ) converges

to the information in ��j(0) if T # 0. It should also be noted that sT is a strictly

increasing function of �1, for any T , so �1 is identi�ed from any sT .

The estimation with s1-data gives implausible results for France and Germany.

For both countries, the estimated k1 is well above 20, which is much higher than

for the other countries and also much higher than the estimate for France based

on micro data, which is about 5 (Bontemps, Robin and Van den Berg, 2000). A

comparison of the empirical distribution of job durations, reveals that F and D

have an unexpectedly high fraction of jobs with a duration of less than or equal

to a year. This is not compatible with the job duration distribution for larger

durations, at least in the current formulation of our model. For France, Cohen,

Lefranc and Saint-Paul (1997) argue that there are jobs with a predetermined

�xed duration, mostly occupied by young workers. In particular, they argue that

one can distinguish two types of job contracts: 1) with a predetermined �xed short

duration, with low �ring and dissolution costs, and low wages, mostly occupied by

new entrants and other young workers and 2) with indeterminate long durations

and high �ring costs. Basically, the type-1 workers bear the burden of the (recent

increases in) labor market exibility.

A possible solution to this problem is to model the heterogeneity in the pop-

ulation, e.g. by allowing for variation in job destruction and/or job o�er arrival

rates.21 Another approach is to use data on separation rates sT for larger T ,

since these are less sensitive to the shape of the job duration density close to

zero. Table 5.9 in OECD (1997) provides the retention rates from 0-<5 years to

5-<10 years of tenure. Retention rates are the mirror-image of separation rates.

Here, they measure the fraction of workers with a tenure less than 5 years who

21We experimented with a model in which the index of search frictions k1 was set at a

particular value and the job destruction rate Æ followed a two-point mixture. This improved

the �t to the observed distribution of job spells.

28

are still with their employer 5 years later. This gives an observation of s5. In

e�ect, we compare 1980{1985 with 1985{1990.

The expression for s5 is the same as for s1, provided we replace Æ and �1 by

5Æ and 5�1, respectively. This gives the results reported in Table 5 on k1 and �1

for Germany and France, which are plausible and (for France) very close to the

results found in micro studies. It is conceivable that the micro studies interpret

part of the short-term temporary jobs as regular jobs. In that case one would

perhaps expect a slightly lower �1 estimate than in the micro studies. In any

case, our results suggest that it would also be important for micro studies to pay

attention to the special nature of these short-term jobs.

There are no data on s5 available for the Netherlands and the US. For the UK,

the estimates based on s5 are rather implausible. Table 5.10 in OECD (1997)

also gives data on s0:25. This gives similar problems for France and Germany as

those based on s1. Moreover, the results for the Netherlands now su�er from the

same problem. The results are reported in Table 5.

A comparison of the �1 estimates in Table 5 to the 87{91 average of the �0estimates in Table 2 shows that there is a positive relation between these rates.

There is a marked di�erence between the EC countries, where the arrival rate in

unemployment is larger than that in employment, and the US where the reverse

inequality holds.

Note that total worker reallocation is of the same order of magnitude for

France and the Netherlands, even though in the Netherlands the job o�er arrival

rate for the employed is substantially higher. In comparison to France, workers

in the Netherlands move relatively quickly to high-wage jobs. However, Æ is

slightly smaller in the Netherlands, and workers stay longer in their high-wage

jobs. As a result, the di�erence between the k1 values of the two labor markets

is not re ected in the cross-sectional reallocation rates, so that these rates may

be uninformative on the mobility potential of the labor market.

This also shows in the results on the decomposition of the total worker real-

location rate. This decomposition is very stable across countries. The fraction

of reallocation due to transitions into and out of unemployment always lies in

the 24%{32% (so the fraction due to job-to-job transitions always lies in the

68%{76% range).

Next, we consider the marginal distribution of elapsed job spells. We �x the

value of the job destruction rate Æ (or its mean) at the average value over the

years 1987{1991. The quasi-ML estimates of k1 from the elapsed job duration

data are implausibly small, and the �t is poor. The estimates are sensitive to

small changes in the value of Æ, but this does not result in a better �t. This

29

con�rms that the elapsed job durations give inaccurate estimates of k1.

To obtain more insight into potential problems with the estimation of the

index of search frictions we use the micro data from the US and France for

conditional (on the wage) inference on the index of search frictions. Figure 6.1

gives the marginal distribution of job durations22 for the two countries and Figure

6.2 kernel estimates of the density of wages.23

The marginal distribution of job durations show that short durations are

indeed overrepresented. In the US that is true for spells up to a year, while in

France spells up to two years are very frequent. The distribution for the US shows

some heaping at years that are multiples of 5. In France there is no evidence of

heaping.

In Section 4.2 we showed that the repeated search model and the steady state

assumption imply that there is a linear relation between the average job spell and

the cdf of the distribution of wages, earned by a cross-section of workers. To check

this relation we grouped wages by 5% intervals and computed the average job

spell for each wage interval. The results are reported in Figure 6.3. We conclude

that the predicted relationship holds surprisingly well. In the US the relation is

slightly convex, which implies that the highest paid workers stay relatively long

on the same job. This is not the case in France.

The relation between the average duration and G can be used to obtain esti-

mates of the index of search frictions and the job destruction rate Æ. We estimate

a linear regression with the average job durations for the 5% intervals as depen-

dent variable and G(w) for that interval as independent variable. The ratio of

the slope and intercept is an estimate of k1. We �nd for the US k1 = 2:551 and

for France k1 = 1:430. The R2 are .98 and 93, respectively, and this con�rms the

close approximation to a linear relation. These estimates are much smaller than

those reported in Table 5. The US index is larger than than French one, so that

the order is unchanged.

The regression estimator is imperfect. In particular, it does not allow us to

consider subsamples obtained by censoring the job spells. In Table 6 we report

ML estimates that estimate k1 as a parameter of the job duration hazard. In the

hazard we substitute the empirical cdf of wages for G.

The estimates from the micro data are smaller than those in Table 5, in

particular for the US. The index k1 is a ratio and the job destruction rate is

larger in the US than in France. Hence, the o�er arrival rates are even with the

estimates in Table 6 much larger in the US. The estimates may be downward

22By year, but 41 means 41 years or longer.23Based on a standard normal kernel and bandwidth 1:06n�:2sw.

30

biased because we use an estimated instead of the population G, so that the

"regressor" in the job hazard is measured with error. The estimates become

larger if we censor the observations progressively. This indicates that the current

speci�cation in which all workers have the same k1 and Æ may be too simple.

We conclude that inference on the index of search frictions is non-trivial. The

sensitivity to the selection of the sample may also explain some of the variation of

estimates of k1 in various studies. Most of the studies minimize the heterogeneity

in the sample by considering a relatively narrow subpopulation, e.g. schoolleavers.

These studies report larger values of k1 than those in Table 6. The estimates

reported in that table are based on a much broader sample. This indicates that

the current practice may be misleading.

6.3 Monopsony indices and decomposition of wage varia-

tion

Wage data. We use categorized data on before-tax monthly wages of full-time

employees who worked during the whole year. For Germany the data refer to

1990.24 For the Netherlands, the data are also for 1990.25 The UK data refer to

1991.26 The US data are from the CPS and are for 1992. The French data are

categorized after-tax wages for 1991.27 The minimum wage and unemployment

bene�ts are taken from CPB (1995). They are converted to local currencies using

the average exchange rate for the particular year.28

We compute the mean and variance of the wage distribution by �tting a

lognormal distribution to the grouped wage data. Next, we compute the mean

and variance of the productivity distribution by equating the estimated mean

and variance to the expressions in section 5. The computation is di�erent for the

EC countries and the US, because in the former �0 > �1, whereas in the latter

the reverse holds. The results for France are for the distribution of after-tax

productivities (on the assumption the tax is nearly proportional, see section 2).

All results are in local currencies. The results are reported in Table 7. They are

based on the estimates of k1 in Table 5. We already noted that these estimates

are not the last word on the size of the index of search frictions for employees.

24Source: L�ohne und Geh�alter, Statistisches Bundesamt, Fachserie 16, Table 12.25The source is Statistisch Jaarboek, 1993, Centraal Bureau voor de Statistiek, Table 31.26Annual Abstract of Statistics, Central Statistical OÆce, Table 6.17.27Les salaires de 1991 �a 1993 dans le secteur priv�e et semi-public, INSEE, 1994, Table 6.28As published in Statistisch Jaarboek, 1994.

31

Table 7 contains the estimates of the monopsony indices. The �rst row gives

the fraction of workers for whom the lowest wage is equal to the minimum wage.

The estimates of the monopsony index are in the second row. The next rows give

counterfactual indices for b = 0, wmin = 0, wmin = b = 0, and k1 = 0. Finally, we

report the fraction of the wage variation due to search frictions.

For all countries the average monopsony power is small. It ranges from less

than 1% in Germany to almost 5% in the UK. For this reason we only consider

counterfactuals that increase the monopsony index. Elimination of unemploy-

ment bene�ts and of the minimum wage increases the monopsony indices to

about 6% for the UK and the Netherlands, but the German index increases to

only 1%. The insensitivity of the German index is due to the relatively high

reservation wages of more productive (unemployed) workers (i.e. the parameter

in equation (12) is relatively small), which in turn is due to a relatively large

value of �0. In the Netherlands and France the e�ect of a reduction in the unem-

ployment bene�ts is somewhat larger than that of a reduction in the minimum

wage. The fraction workers for whom the minimum wage is binding is larger in

these countries. We conclude from this that a concentration of wages near the

minimum wage is not a good predictor of the importance of bene�ts and the

minimum wage on monopsony power. A decrease in b a�ects not only low, but

also higher productivity workers. The index for the counterfactual k1 = 0 (the

minimum wage is unchanged, because otherwise this index would be 1) shows

convincingly that the main protection of workers against the monopsony power

of �rms is provided by the ability to move to high-wage jobs.

In all countries, the unemployment bene�ts and the minimum wage reduce the

monopsony power of �rms, i.e. make the labor market more like a competitive

market where wages are equal to (marginal) products. The case of the Nether-

lands that has a high minimum wage and high unemployment bene�ts illustrates

this point. Without these wage oors the labor market becomes more monop-

sonistic. However, the price that is paid for these wage oors is a high amount

of structural unemployment among less productive workers. Indeed, there are

good reasons to suspect that structural unemployment in the Netherlands is

even higher than our estimate, since many structurally unemployed are counted

as non-participants on the labor market (they are in early retirement or in the

disability program; see e.g. Koning, Ridder and Van den Berg, 1995, and Van

den Berg and Ridder, 1998). It should be noted that the estimates of k1 for the

Netherlands are very close to the estimates in micro studies (Van den Berg and

Ridder, 1998). Our estimate of �0 is somewhat higher than in the micro studies,

but this can be attributed to the fact that the micro studies do not allow for

32

structural unemployment, whereas here we do. Although our model is too simple

to allow for a welfare analysis of the minimum wage, it is clear that the argument

that the minimum wage is needed to protect workers against monopsonistic em-

ployers is not convincing. Of course, our analysis does not allow for individual

variation in the rate of job-to-job transitions, but on average these transitions

seem to protect the workers suÆciently.

The case of Germany illustrates another mechanism to strengthen the position

of workers relative to employers. The low job destruction rate in that country,

that may well be a consequence of the high level of employment protection (see

Table 1), increases the reservation wages of more productive workers and reduces

the monopsony index.

Finally, we note that, as expected, most of the wage variation is not explained

by search frictions, but by productivity variation. By this measure, the UK and

US labor markets are close to competitive.

7 Conclusion

In this paper we have de�ned and estimated measures of labor market imper-

fection in the context of an equilibrium search and matching framework. The

method uses readily available aggregate data on marginal distributions of unem-

ployment and job durations and wages. Estimation of some of the characteristics

is invariant to the way in which wage determination is modeled. The estimation

results provide some insights into the performance of the labor markets in the

USA, the UK, France, Germany and the Netherlands.

The data that we use in the calibration are collected yearly in the Current

Population Survey (CPS) in the US and the Labor Force Survey (LFS) in EC

countries. These surveys concentrate on labor market ows and wages. Our

framework relates these seemingly unrelated data to key policy parameters as the

level of unemployment bene�ts, the minimum wage, and the level of employment

protection.

The accuracy of our estimates is limited by the availability of published ag-

gregate data. For instance, the LFS collects job tenure data, but these are not

routinely published.

The main problem is the estimation of our index of search frictions. We show

that data on the joint distribution of wages and job durations are informative,

but that the resulting estimates are lower than those obtained from micro panel

studies. The latter often use highly selective samples, and this may be part of

the explanation for the di�erent estimates. The reconciliation of these estimates

33

is an important topic for future research, because the predictions of the basic

search model are surprisingly accurate.

Another weak point is the estimate of the job destruction rate. Data on the

fraction of job leavers who become unemployed would help in the estimation of

that rate. Although the details of our model and the calibration may be criticized,

we think that our approach directs attention to some key parameters that may

help us understand the di�erences between labor markets.

Several topics emerge for further research. It would be interesting to examine

models with more policy parameters. This may actually imply that some of the

more elegant methods for empirical inference would have to be replaced by meth-

ods that require more explicit model speci�cations. It would also be interesting

to estimate models for a large series of di�erent time periods. Preferably, these

periods would have to be so far apart that they can be seen as two di�erent equi-

libria. We could exploit variation across time to identify endogenized job o�er

arrival rates.

34

Table 1: Some characteristics of the labor markets in the �ve OECD

countries

NL D F UK USA

Average standardized

unemployment rate (1989{

1993)

6.9 5.1 9.9 8.7 6.2

Monthly ow out of unempl.

(% of unempl.; av. over

1985 and 1993)

6.6 7.6 3.6 7.7 39.4

Monthly ow into unempl.

(% of empl.; av. over 1985

and 1993)

.26 .41 .33 .59 2.26

Monthly ow of hires (% of

empl.; av. various years)

.99 2.63 2.42 { 5.38

Average wedge (%) 44 41 38 29 33

Minimum wage (max.

of statutory and collective;

Dutch guilders per year)

30833 21875 23750 15416 16607

Min. wage as frac. wage av.

production worker

.57 .38 .63 .39 .35

Average minimum unempl.

bene�t (Dutch guilders per

year)

25932 20862 16598 12670 12704

Employment protection

ranking

3 5 4 2 1

Germany is West-Germany only; Average standardized unemployment rate, OECD (1995), p.

216; Monthly out ow from and in ow into unemployment, OECD (1995), p. 27{28; Monthly

ow of new hires, OECD (1997), p. 166; Replacement rate, average wedge, minimum wage,

wage average production worker, and minimum unemployment bene�t (average of one-earner

family with two children and single person), CPB (1995); employment protection ranking from

OECD (1994), p. 74.

35

Table 2: O�er arrival rate (per month) (�0) and average unemployment

duration (months) of frictionally unemployed, for �ve OECD countries,

1983{94

NL D F UK US

Year �0 av. dur. �0 av. dur. �0 av. dur. �0 av. dur. �0 av. dur.

83 .0580 17.2 .0770 13.0 .0701 14.3 .0794 12.6 .405 2.5

84 { { .0712 14.0 .0782 12.8 .0947 10.6 .497 2.0

85 .0613 16.3 .0804 12.4 .0635 15.7 .0967 10.3 .527 1.9

86 { { .0825 12.1 .0713 14.0 .0988 10.1 .516 1.9

87 .110 9.1 .0940 10.6 .0723 13.8 .114 8.8 .534 1.9

88 .109 9.2 .0975 10.3 .0775 12.9 .124 8.1 .565 1.8

89 .113 8.9 .0896 11.2 .0789 12.7 .139 7.2 .599 1.7

90 .120 8.4 .0975 10.3 .0933 10.7 .156 6.4 .563 1.8

91 .128 7.8 .101 9.9 .0936 10.7 .153 6.5 .468 2.1

92 .0594 16.8 .0981 10.2 .116 8.6 .105 9.6 .420 2.4

93 .0478 21.0 .0851 11.8 .110 9.1 .0849 11.8 .442 2.3

94 .0664 15.1 .0797 12.6 .0957 10.4 .0950 10.5 .408 2.5

36

Table 3: Fraction of unemployment that is structural (�) and job de-

struction rate (per month) (Æ) for �ve OECD countries, 1983{94

NL D F UK US

Year � Æ � Æ � Æ � Æ � Æ

83 .000 .00783 .000 .00526 .010 .00595 .13 .00862 .17 .0357

84 { { .036 .00493 .076 .00759 .23 .00892 .15 .0342

85 .20 .00575 .15 .00504 .035 .00704 .24 .00956 .12 .0360

86 { { .19 .00471 .12 .00714 .23 .00992 .11 .0347

87 .24 .00923 .23 .00529 .15 .00754 .26 .0105 .11 .0315

88 .28 .00809 .23 .00504 .16 .00737 .27 .00899 .093 .0298

89 .30 .00766 .22 .00422 .16 .00701 .24 .00837 .076 .0310

90 .28 .00733 .22 .00391 .18 .00798 .22 .00912 .073 .0304

91 .26 .00750 .21 .00339 .16 .00792 .15 .0122 .080 .0309

92 .048 .00335 .047 .00629 .12 .0116 .092 .0102 .14 .0288

93 .00 .00321 .058 .00669 .089 .0129 .11 .00872 .15 .0274

94 .16 .00431 .092 .00689 .071 .0129 .19 .00829 .13 .0230

37

Table 4: Total and structural unemployment rate (%), for �ve OECD

countries, 1983{94

NL D F UK US

Year Total Struct. Total Struct. Total Struct. Total Struct. Total Struct.

83 11.9 0.0 6.4 0.0 7.9 .1 11.1 1.4 9.6 1.6

84 12.4 { 6.7 .2 9.5 .7 10.9 2.5 7.5 1.1

85 10.5 2.1 6.9 1.0 10.3 .4 11.5 2.8 7.2 .9

86 10.0 { 6.6 1.3 10.2 1.2 11.5 2.6 7.0 .8

87 10.0 2.4 6.8 1.6 10.7 1.6 11.0 2.9 6.2 .7

88 9.4 2.6 6.3 1.4 10.2 1.6 9.0 2.4 5.5 .5

89 8.8 2.6 5.7 1.3 9.6 1.5 7.4 1.8 5.3 .4

90 7.8 2.2 4.9 1.1 9.4 1.7 7.0 1.5 5.5 .4

91 7.3 1.9 4.1 .9 9.2 1.5 8.6 1.3 6.7 .5

92 5.6 .3 6.3 .3 10.2 1.2 9.7 .9 7.4 1.0

93 6.3 0.0 7.7 .4 11.4 1.0 10.3 1.1 6.8 1.0

94 7.2 1.2 8.7 .8 12.7 .9 9.7 1.8 6.1 .8

38

Table 5: Index of search frictions

�1 k1 total worker reallocation

Netherlands 0.072 9.1 0.026

Germany 0.028 6.5 0.013

France 0.038 5.0 0.025

United Kingdom 0.13 13 0.047

United States 0.61 20 0.13

Table 6: Estimate of index of search frictions from conditional hazard;

job durations censored at year C

Uncensored C = 20 C = 5 C = 2

United States 2.498 3.062 4.645 6.062

France 1.348 2.648 4.176 4.689

39

Table 7: Mean and standard deviation of wage and productivity distri-

butions (local currencies)

Wage distribution Productivity distribution

Mean Standard dev. Mean Standard dev.

Netherlands 4066 1468 4186 1533

Germany 4143 1735 4172 1751

France 8962 4012 9188 4169

United Kingdom 1213 601 1272 623

United States 2348 1432 2436 1483

40

Table 8: Fraction of workers for whom the lowest wage in the market

is the minimum wage rather than the reservation wage of the unem-

ployed, (counterfactual) monopsony power indices, and the fraction of

wage variation due to search frictions

Germany Netherlands France United Kingdom United States

Frac. min. wage .016 .22 .093 .74 1.

� .0068 .029 .025 .046 .036

�b=0 .010 .034 .037 .046 .036

�wmin=0 .0070 .031 .027 .047 .040

�wmin=b=0 .011 .060 .046 .063 .053

�k1=0 .62 .44 .52 .69 .68

Frac. var. frictions .004 .041 .019 .061 .039

41

Figure 1: Frequency distribution job durations; US (top) and France

(bottom), 1991

42

Figure 2: Kernel estimates density monthly gross wages; US (top) and

France (bottom), 1991

43

Figure 3: Average job duration by 5% wage intervals; US (top) and

France (bottom), 1991

44

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47

Appendix

A1. Proof of Proposition 1

Consider the job spells t�j of a cohort of workers who just started in a new job

after leaving unemployment or after leaving their previous job (J-in ow). We call

this a J-in ow sample of job durations. The density of t�j given the wage w on

the job is of course the same as for tuj given w,

'(t�jjw) = (Æ + �1F (w))e�(Æ+�1F (w))t�j

We now need to determine the distribution of w in the J-in ow. At a given

point in time, the fraction of frictionally unemployed workers is Æ=(Æ + �0). This

is a fraction of the workers that are active, i.e. of (1�q)m. Of these, �0dt receive

a job o�er in a small interval with length dt. The corresponding wage o�er has

density f(w). Consequently, the joint probability density of the events of being

unemployed, receiving a job o�er and owing into a job with wage w equals

Æ

Æ + �0�0f(w) (15)

At the same point of time, the fraction of employed workers is �0=(Æ + �0).

(Again, this is a fraction of the workers that are active, i.e. of (1 � q)m.) The

density of wages w0 among them is g(w0), which is the density associated with

G. Of these workers, �1dt receive a job o�er in a small interval with length

dt. The corresponding wage o�er has density f(w). This o�er is acceptable

if w > w0. Consequently, the joint probability density of the events of being

employed, earning a wage w0, receiving a job o�er, accepting it, and subsequently

earning a wage w equals

�0

Æ + �0g(w0)�1F (w0)

f(w)

F (w0)I(w0 < w <1) (16)

in which I(.) is the indicator function of the event between parentheses. By the

law of total probability we add (15) and (16) to obtain the joint density of w

and w0. The density of w in the J-in ow follows by integration over w0. In the

steady-state, i.e. if worker ows in and out all states are equal, the density g

can be expressed in terms of F and the frictional parameters (see equation (3) in

subsection 2.1). As a result, the proposition follows.

A2. Alternative theoretical frameworks

We examine to what extent our measures of imperfection make sense in the

context of other theories with informational frictions and search on the job, and

to what extent the estimates are biased in the context of those theories. We will

mostly focus on the index of search frictions and the estimation of �1.

First of all, Abbring (1998) extends the basic Pissarides (1990) job matching

model by allowing for search on the job. In this model, the wage is determined

in decentralized bargaining between worker and �rm (a �rm here equals a single

vacancy or job). Given certain assumptions on the way a currently employed

worker can negotiate with another �rm, the equilibrium is such that all contacts

result in a match. Each time an employed worker meets another �rm, the worker

moves to the new �rm, and his wage increases. In this model, the hazard rate

of the job duration distribution is simply equal to �1 + Æ, independently of the

current wage. If this model is correct then our estimation method actually over-

estimates �1. It should be noted that in this model (as well as in the models of

the following paragraphs) the concepts of structural and frictional unemployment

are still meaningful if the labor market consists of separate segments. The arrival

rates �0 and �1 are endogenized in job matching models, so what we estimate are

the actual values of contact rates. In the Abbring (1998) model, the monopsony

power index in a single segment can be shown to be almost the same as before.

The only di�erence concerns the fact that k1 has to be replaced by �k1, with �

being the parameter that gives the part of the match surplus that goes to the

worker.

Secondly, consider the model by Mortensen (1994), who extends the basic

Pissarides (1990) model by allowing 1) for stochastic idiosyncratic productivity

shocks on the job29 (this is actually the model in Mortensen and Pissarides, 1994)

and 2) for on-the-job search. In this model, new jobs are the most productive

because they employ the latest technology. On-the-job search is somewhat more

restricted than in Abbring (1998), since search by workers who are employed in a

job with the highest productivity is ruled out. This means that a worker starts to

search on the job after the moment that the productivity of his job experiences

the �rst shock, which by de�nition is a negative shock. As a result, the job-to-job

transition rate is zero for jobs with duration zero. The hazard of the job duration

distribution starts at Æ and then gradually increases. If this model is correct

29The models of section 2 can also be interpreted as allowing for such shocks. If a job has

two possible productivity levels, one of which is unpro�table, then a drop in the productivity

level results in a dismissal; this occurs at rate Æ.

then our estimation method should produce an estimate of �1 equal to zero, or

at least it would under-estimate the rate at which searching employed workers

meet vacancies.

Thirdly, consider the model by Pissarides (1994). He extends the basic Pis-

sarides (1990) model by distinguishing between two productivity levels and by

allowing for on-the-job search. Again, search by workers in a job with the highest

productivity is ruled out. In addition, job-searching workers in low-productivity

jobs only consider matches with high-productivity �rms. Both types of jobs al-

low for the accumulation of job-speci�c human capital. As a result, the only

type of job-to-job transitions that occur are transitions from workers in a low-

productivity job with a short elapsed duration to a high-productivity job. The

job duration distribution is a mixture of an exponential distribution with param-

eter Æ (these are the high-productivity jobs) and a distribution with a hazard that

decreases until it reaches Æ (these are the low-productivity jobs). It is diÆcult to

determine which model variable corresponds to �1. In any case, the arrival rate

for searching employees depends crucially on the proportion of high- and low-

productivity �rms. In the models of Mortensen (1994) and Pissarides (1994), the

wage is not constant in a job. This makes it diÆcult to derive a simple measure

of monopsony power.

Finally, consider the extension of the Burdett and Mortensen (1998) equilib-

rium search model where workers are inherently within-market heterogeneous in

their opportunity costs of leisure or their unemployment bene�ts (see Bontemps,

Robin and Van den Berg, 1999, for a model with within-market heterogeneity of

both workers and �rms). In this model, some unemployed workers reject some

wage o�ers because they are lower than their reservation wage. As a result,

employed individuals will on average reject more o�ers of new jobs than in the

models of section 2. Our estimation method will then under-estimate �1.

The studies above vary widely in their predicted e�ect on the bias of the

estimate of �1. The most we can say is that if this estimate is biased then it is

not clear from the theoretical literature whether it is biased upward or downward.

The measures of structural and frictional unemployment that we developed are

however robust with respect to the alternative model speci�cations. For most

studies, it is diÆcult to summarize the monopsony power in a transparent way.30

30In all fairness, it should be noted that most models mentioned here abstract from some of the

phenomena that are observed in micro duration and transition data and that are incorporated

in equilibrium search models. Some studies do not consider on-the-job search, whereas others

make predictions on the job hazard rate as a function of tenure or the wage that are not

commonly observed.

A3. Monopsony power index if the lowest wage is always equal to the

minimum wage

We assume that all workers have � < wmin = w, so, in terms of the classi�cation

used in Section 5, they are all in case (ii). As a result, E(wjp) = (k1p+wmin)=(k1+

1). By taking the expectation of this across all segments we obtain

E(w) =k1

1 + k1E(p) +

1

1 + k1wmin (17)

with E(p) denoting the mean of the distribution of p truncated at wmin. Equation

(17) can be used to express E(p) in terms of the mean wage, the minimum wage,

and the index k1 of search frictions. This in turn can be substituted into (9) to

obtain an estimate of �.

As mentioned in Section 1, there are basically two factors preventing the

employers to attain a monopoly pro�t: the wage oor, and search on the job.

The average monopsony power captures the combined e�ect of these two factors.

Now let us examine the two counterfactual cases in which one of these two factors

is absent. First, suppose there is no wage oor in the labor market (so there is

no mandatory minimum wage, and w = 0). At �rst sight it may seem to be

impossible to obtain any results here, since we do not know the shape of the

productivity density below the original minimum wage wmin, and we need that

in order to calculate the new E(p). However, substitution of (17) with wmin = 0

into (9) gives �nowage oor = 1=(1 + k1), which is identi�ed. Moreover, this result

holds for any distribution of p.

In the second counterfactual case, there is no search on the job (so k1 = 0).

Then all wages are equal to wmin, but the distribution of p in the labor market

does not change. As a result, we can use our estimate of E(p) again. Substitution

of this estimate and of w � wmin into (9) gives an estimate of �k1=0. In the

following equations, the quantities on the right-hand sides refer to observed data

and estimates based on observed data.

� =E(w)� wmin

(1 + k1)E(w)� wmin

�nowage oor =1

1 + k1

�k1=0 =(1 + k1)(E(w)� wmin)

(1 + k1)E(w)� wmin

Finally, recall that if there is no wage oor and search on the job is absent, then

� = 1, whereas if there are no search frictions then � = 0.

By confronting the estimate of � to those of �nowage oor and �k1=0 we can

quantify the relative importance of the minimum wage and search on the job in

the actual monopsony power. Note that due to the nonlinear nature of the model,

this is not an additive decomposition. In fact, the decomposition is multiplicative,

as is obvious from the three expressions above. The estimation results are below.

Average monopsony power

� �nowage oor �k1=0

West Germany 0.08 0.13 0.57

Netherlands 0.04 0.10 0.45

France 0.07 0.17 0.43

United Kingdom 0.05 0.07 0.70

United States 0.03 0.05 0.72

Again, the actual average monopsony power does not vary much between

the �ve countries. However, the decomposition of the average monopsony power

enables a distinction into two groups of countries. For the UK and the US, the

minimum wage is much less important as a tool to curb average monopsony power

than the fact that job-to-job transitions are possible. For the other countries,

the minimum wage is more important. However, for all countries, job-to-job

transitions are more important than the minimum wage.

France and Germany are characterized by very low worker turnover. However,

recall that we have ignored the high amount of very short job durations. Basically,

for these countries we focus on the rather in exible labor markets for prime-aged

and older individuals. These labor markets show very little job-to-job turnover,

and as a result the employers have a relatively large monopsony power (our

method actually over-estimates k1 for these markets). Raising the minimum wage

would reduce this power, but this would be at the expense of a higher structural

unemployment. In light of the fact that most other countries considered have a

(sometimes much) higher job o�er arrival rate in employment, there seems to be

scope for policies aimed at increasing this rate.

A4. Heterogeneity in Æ and the �t to the elapsed job duration data

Assume that Æ has a discrete distribution with two points of support Æ1 and Æ2,

with the proportion of Æ1-types in the J-in ow equal to P . The density of elapsed

job spells is then a mixture of densities of incomplete job spells, with fraction of

Æ1-types equal to

eP =P

Æ1PÆ1+ P

Æ2

The mean of the distribution of the job destruction rate is set equal to the mean

over the years 1987{1991 in Table 3. This mean is identi�ed from the hazard of

the tenure distribution at very long spells, but censoring and recall errors make

an estimate based on the grouped spell distribution unreliable.31 The estimation

results obtained with the elapsed job duration data are reported below.

The distribution of the job destruction rate (mean �xed at average

estimate 1987{91) and �tted and observed fractions, for �ve OECD

countries, 1995

Distr. Æ Fitted (observed) fractions

Æ1 Æ2 frac. Æ1 0{1 1{2 2{5 5{10 10{20 20{

NL .0763 .00481 .04 .163 .109 .220 .178 .126 .204

(.163) (.114) (.204) (.198) (.118) (.203)

D .0225 .00362 .18 .155 .107 .204 .186 .178 .171

(.161) (.094) (.220) (.172) (.184) (.170)

F .0509 .00361 .08 .136 .088 .182 .193 .201 .199

(.150) (.080) (.177) (.174) (.233) (.187)

UK .107 .00526 .04 .189 .118 .226 .198 .165 .104

(.196) (.107) (.195) (.235) (.173) (.094)

US .228 .00505 .11 .257 .107 .203 .179 .153 .102

(.260) (.085) (.200) (.198) (.168) (.090)

The results con�rm the suspicions regarding the composition of the stock of jobs:

a relatively small fraction is short-lived while the majority of jobs has a much

lower destruction rate. The fraction of short-lived jobs in the J-in ow is larger.

31Estimation of the hazard in the open interval on the (erroneous) assumption that elapsed

job spells are exponentially distributed after 20 years, gives an estimate that is close to the

average over 87{91, except for Germany and the US. The exponential tail estimate is larger

than the average in Germany and smaller than the average in the US.